For clarification purposes, the router is a US Robotics 8004 and our cable modem is a Motorola SB5100. Hope that helps out a bit. So really, neither of those is our router....

What else is connected to the router?

http://forums.techguy.org/reviews/426207-us-robotics-8004-firewall-router.html

Nice. This guy had the same problem; seems as if the firewall misidentifies UDP traffic as some sort of attack.

Want to try turning off the firewall on the router?

I'll dig up what I can to try to get a workaround for this in the client.

We didn't have a problem until the 1.5.9 client. Same router and everything. Nothing changed except for the update.

The update may very well have changed the way Vendetta appears to your firewall. This happens on every update with my software firewall. Try (briefly) shutting down the firewall and connecting with Vendetta. This will go far to help troubleshoot the issue.